Question 1011341
RT=J to relate work rate, time, amount of job


First examine their rates, as 1 job per quantity of time in hours
<pre>
Roofer             1/14

Assistant          1/x

Both together      1/6
</pre>

{{{1/14+1/x=1/6}}}
{{{2*3*7x/14+2*3*7x/x=2*3*7*x/6}}}
{{{3x+42=7x}}}
{{{4x=42}}}
{{{2x=21}}}
{{{x=21/2}}}  or 10&1/2.
You can use this rate as  {{{highlight_green(1/x=2/21)}}}.


Next, the work to be done is cut into two time periods using different arrangements of roofer and assistant.  Let t be the time asked for.
-
{{{highlight((1/6)2+(2/21)t=1)}}}.
Important is this equation make sense and the earlier rate analysis make sense.  Now just solve for t.